SOLUTION: Find 2 positive real numbers that differ by 2 and have a product of 10.

Question 298679: Find 2 positive real numbers that differ by 2 and have a product of 10.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Find 2 positive real numbers that differ by 2 and have a product of 10.
.
Let x = smaller of two positive real number
then
x+2 = larger of two positive real number
.
x(x+2) = 10
x^2+2x = 10
x^2+2x-10 = 0
.
Since we can't factor, we must resort to the quadratic formula giving us:
x = {2.317, -4.317}
Since the problem want "positive" numbers our solution is:
x = 2.317
The other number is then
2.317 + 2 = 4.317
.
The two numbers are 2.317 and 4.317
.
Details of quadratic formula follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=44 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.3166247903554, -4.3166247903554. Here's your graph:

RELATED QUESTIONS
Find two positive real numbers that differ by 2 and have a product of 10. (answered by checkley77)

Find two positive real numbers that differ by 2 and have a product of... (answered by orca)

Find two positive real numbers that differ by 2 and have a product of... (answered by richwmiller,Fombitz)

Find two positive real numbers that differ by 2 and have a product of... (answered by checkley77)

2 positive real numbers that differ by 1 and have a product of... (answered by ankor@dixie-net.com)

Find two positive real numbers that differ by 1 and have a product of 1. (answered by longjonsilver)

Find two positive real numbers that differ by 1 and have a product of... (answered by longjonsilver)

Find two positive real numbers that differ by 1 and have a product of... (answered by stanbon)

find two positive real numbers that differ by 1 and have a product of... (answered by ankor@dixie-net.com)